conclusion of flow measurement experiment

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Experiment #2: Bernoulli’s Theorem Demonstration

1. introduction.

Energy presents in the form of pressure, velocity, and elevation in fluids with no energy exchange due to viscous dissipation, heat transfer, or shaft work (pump or some other device). The relationship among these three forms of energy was first stated by Daniel Bernoulli (1700-1782), based upon the conservation of energy principle. Bernoulli’s theorem pertaining to a flow streamline is based on three assumptions: steady flow, incompressible fluid, and no losses from the fluid friction. The validity of Bernoulli’s equation will be examined in this experiment.

2. Practical Application

Bernoulli’s theorem provides a mathematical means to understanding the mechanics of fluids. It has many real-world applications, ranging from understanding the aerodynamics of an airplane; calculating wind load on buildings; designing water supply and sewer networks; measuring flow using devices such as weirs, Parshall flumes, and venturimeters; and estimating seepage through soil, etc. Although the expression for Bernoulli’s theorem is simple, the principle involved in the equation plays vital roles in the technological advancements designed to improve the quality of human life.

3. Objective

The objective of this experiment is to investigate the validity of the Bernoulli equation when it is applied to a steady flow of water through a tapered duct.

In this experiment, the validity of Bernoulli’s equation will be verified with the use of a tapered duct (venturi system) connected with manometers to measure the pressure head and total head at known points along the flow.

5. Equipment

The following equipment is required to complete the demonstration of the Bernoulli equation experiment:

• F1-10 hydraulics bench,
• F1-15 Bernoulli’s apparatus test equipment, and
• A stopwatch for timing the flow measurement.

6. Equipment Description

The Bernoulli test apparatus consists of a tapered duct (venturi), a series of manometers tapped into the venturi to measure the pressure head, and a hypodermic probe that can be traversed along the center of the test section to measure the total head. The test section is a circular duct of varying diameter with a 14° inclined angle on one side and a 21° inclined angle on other side. Series of side hole pressure tappings are provided to connect manometers to the test section (Figure 2.1).

Manometers allow the simultaneous measurement of the pressure heads at all of the six sections along the duct. The dimensions of the test section, the tapping positions, and the test section diameters are shown in Figure 2.2. The test section incorporates two unions, one at either end, to facilitate reversal for convergent or divergent testing. A probe is provided to measure the total pressure head along the test section by positioning it at any section of the duct. This probe may be moved after slackening the gland nut, which should be re-tightened by hand. To prevent damage, the probe should be fully inserted during transport/storage. The pressure tappings are connected to manometers that are mounted on a baseboard. The flow through the test section can be adjusted by the apparatus control valve or the bench control valve [2].

Bernoulli’s theorem assumes that the flow is frictionless, steady, and incompressible. These assumptions are also based on the laws of conservation of mass and energy.  Thus, the input mass and energy for a given control volume are equal to the output mass and energy:

These two laws and the definition of work and pressure are the basis for Bernoulli’s theorem and can be expressed as follows for any two points located on the same streamline in the flow:

P: pressure,

g: acceleration due to gravity,

v : fluid velocity, and

z: vertical elevation of the fluid.

In this experiment, since the duct is horizontal, the difference in height can be disregarded, i.e., z 1 =z 2

The hydrostatic pressure (P) along the flow is measured by manometers tapped into the duct. The pressure head (h), thus, is calculated as:

Therefore, Bernoulli’s equation for the test section can be written as:

The total head (h t ) may be measured by the traversing hypodermic probe. This probe is inserted into the duct with its end-hole facing the flow so that the flow becomes stagnant locally at this end; thus:

The conservation of energy or the Bernoulli’s equation can be expressed as:

The flow velocity is measured by collecting a volume of the fluid (V) over a time period (t). The flow rate is calculated as:

The velocity of flow at any section of the duct with a cross-sectional area of  is determined as:

For an incompressible fluid, conservation of mass through the test section should be also satisfied (Equation 1a), i.e.:

8. Experimental Procedure

• Place the apparatus on the hydraulics bench, and ensure that the outflow tube is positioned above the volumetric tank to facilitate timed volume collections.
• Level the apparatus base by adjusting its feet. (A sprit level is attached to the base for this purpose.) For accurate height measurement from the manometers, the apparatus must be horizontal.
• Install the test section with the 14° tapered section converging in the flow direction. If the test section needs to be reversed, the total head probe must be retracted before releasing the mounting couplings.
• Connect the apparatus inlet to the bench flow supply, close the bench valve and the apparatus flow control valve, and start the pump. Gradually open the bench valve to fill the test section with water.
• Close both the bench valve and the apparatus flow control valve.
• Remove the cap from the air valve, connect a small tube from the air valve to the volumetric tank, and open the air bleed screw.
• Open the bench valve and allow flow through the manometers to purge all air from them, then tighten the air bleed screw and partly open the bench valve and the apparatus flow control valve.
• Open the air bleed screw slightly to allow air to enter the top of the manometers (you may need to adjust both valves to achieve this), and re-tighten the screw when the manometer levels reach a convenient height. The maximum flow will be determined by having a maximum (h 1 ) and minimum (h 5 ) manometer readings on the baseboard.

If needed, the manometer levels can be adjusted by using an air pump to pressurize them. This can be accomplished by attaching the hand pump tube to the air bleed valve, opening the screw, and pumping air into the manometers.  Close the screw, after pumping, to retain the pressure in the system.

• Take readings of manometers h 1 to h 6 when the water level in the manometers is steady. The total pressure probe should be retracted from the test section during this reading.
• Measure the total head by traversing the total pressure probe along the test section from h 1 to h 6 .
• Measure the flow rate by a timed volume collection. To do that, close the ball valve and use a stopwatch to measure the time it takes to accumulate a known volume of fluid in the tank, which is read from the sight glass. You should collect fluid for at least one minute to minimize timing errors. You may repeat the flow measurement twice to check for repeatability. Be sure that the total pressure probe is retracted from the test section during this measurement.
• Reduce the flow rate to give the head difference of about 50 mm between manometers 1 and 5 (h 1 -h 5 ). This is the minimum flow experiment. Measure the pressure head, total head, and flow.
• Repeat the process for one more flow rate, with the (h 1 -h 5 ) difference approximately halfway between those obtained for the minimum and maximum flows. This is the average flow experiment.
• Reverse the test section (with the 21° tapered section converging in the flow direction) in order to observe the effects of a more rapidly converging section. Ensure that the total pressure probe is fully withdrawn from the test section, but not pulled out of its guide in the downstream coupling. Unscrew the two couplings, remove the test section and reverse it, then re-assemble it by tightening the couplings.
• Perform three sets of flow, and conduct pressure and flow measurements as above.

9. Results and Calculations

Please visit this link for accessing excel workbook for this experiment.

9.1. Results

Enter the test results into the Raw Data Tables.

Raw Data Table

  Raw Data Table

9.2 calculations.

For each set of measurements, calculate the flow rate; flow velocity, velocity head, and total head,  (pressure head+ velocity head).  Record your calculations in the Result Table.

Result Table

Use the template provided to prepare your lab report for this experiment. Your report should include the following:

• Table(s) of raw data
• Table(s) of results
• For each test, plot the total head (calculated and measured), pressure head, and velocity head (y-axis) vs. distance into duct (x-axis) from manometer 1 to 6, a total of six graphs. Connect the data points to observe the trend in each graph. Note that the flow direction in duct Position 1 is from manometer 1 to 6; in Position 2, it is from manometer 6 to 1.
• Comment on the validity of Bernoulli’s equation when the flow converges and diverges along the duct.
• Comment on the comparison of the calculated and measured total heads in this experiment.
• energy loss and how it is shown by the results of this experiment, and

Applied Fluid Mechanics Lab Manual Copyright © 2019 by Habib Ahmari and Shah Md Imran Kabir is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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VENTURI METER AND ORIFICE PLATE LAB REPORT

Venturi meter effect and orifice plate effects are two main and very important phenomena in the fluid mechanics sub-field of mechanical engineering. 

In this post, the effect of the venturi meter and orifice plate on the fluid flow will be discussed and complete work will be presented in the form of a report. 

According to Michael Reader-Harris (n.d), a Venture meter is an instrument used to study the flow of fluid when it passes through the converging section. 

There is an increase in the velocity and decrease in the pressure of the flowing fluid when the area available to flowing fluid decreases, this effect is called the venture effect named after the physicist who first introduces this theory. 

According to Michael Reader-Harris (n.d), an Orifice plate is an instrument used for three different applications one to measure the flow rate, second to restrict the flow, ad third to reduce the pressure of the flowing fluid. 

It depends on the orifice plate-associated calculation method that either the mass flow rate or the volumetric flow rate is used for calculation. 

It uses the Bernoulli experiment which shows the relationship between velocity and pressure for a flow of fluid . When one increases then the second one decrease.

• The Thin Plate, Concentric Orifice
• Eccentric Orifice Plates
• Segmental Orifice Plates
• Quadrant Edge Plate
• Conic Edge Plate

Theory of  Venturi Meter and Orifice Plate

Procedure  venturi meter and orifice plate.

To set up the orifice tube and venture meter apparatus two tubes were connected one on each of the outlet and inlet of the apparatus. 

The tube which was connected to the venture meter outlet was further connected to the measuring tank. 

To level the orifice meter and venture tube apparatus, adjustable screws are provided at the apparatus.

The apparatus was connected to the power source to run the motor for the water supply. The bench valve and the control valve of the apparatus were open to let the water move into the tube and to remove all the air pockets.

To raise the water level in the manometer tubes the control valve was closed gradually and when the height of the water level was enough high then the bench valve was gradually closed. 

With both valves closed there was static water in the meter at a moderate pressure

The flow rate of the water was recorded and the height of the water level was also recorded in all the tubes

The difference between the heights of the water level and the flow rate will change upon opening any one of the apparatus valves. 

The flow rate was calculated by noticing the time required to fill the tank of a known weight and at the same time the level of the water in the manometer tubes was also recorded

The same process is repeated for different flow rates

Sample Calculations for Venturi Meter and Orifice Plate

Experimental results  venturi meter and orifice plate.

Discussion Venturi Meter and Orifice Plate

2. Result shows that with a decrease in the flow rate, the value of the ∆h also decreases. So it can be said from the results that the difference in the height of the water level is directly proportional to the flow rate.

3. Change in the height of the water column of the venture meter is much less than the change in the height of the water column in the orifice plate this is because the difference in diameter of the areas of the orifice is much more than the venture meter. 

So we can say that the difference in height of the water column is directly proportional to the difference in the diameter of the area.

Conclusion  Venturi Meter and Orifice Plate

An experiment was conducted to find the overall meter coefficient C in the venture meter and orifice tube and results show that the flow rate and ∆h are directly proportional to each other and along with this ∆h and the ∆d are also directly proportional to each other. Both these things are important as they are used to calculate the overall meter coefficient C

4 comments:

error analysis?

NICE INFORMATION

Thank you so much. This will really help with my Lab report!!

• Instrumentation Engineering
• Flow Measurement

Methods of Flow Measurements

• Affiliation: Heriot-Watt University

• Baku Higher Oil School

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CHE241 Fluid Mechanics- Lab Report Flowmeter Measurement Apparatus

Related Papers

Nurlina Syahiirah

Objective : 1) To obtain the flow rate measurement by utilizing three basic types of flow measuring techniques such as rotameter, venturI meter and orifice meter. Abstract : SOLTEQ® Flowmeter Measurement Apparatus (Model: FM101) is designed to measure a flow of an incompressible fluid. From this experiment, we will obtain the flow rate measurement with comparison of pressure drop by using the three basic types of flow measuring techniques which are ratometer, venturi meter and orifice meter and compare the accuracy of the three techniques. Actual flow rates for the water is determined by using a constant volume of 3L and the time taken for the water to reach until 3L for each experiment. The flow rates of the flowmeter could be compared based on the results that we get from the plotted graph. It shows that venturi meter is more accurate compare to orifice meter which the flow rates of venturi meter is closer to the actual value of the flow rates. Overall, our experiment was successfully done

vic olawepo

Frezer Belay

The complete laboratory includes parts 1 to 5 and any part can be supplied individually or additionally. (Base Service Unit + Module/s is the minimum supply)

Akshay Patel

Mohammed Ziauddin Ahmed

samson svondo

This is an experimental write up for the calibration of flow meters as observed and carried out at the National University of Science of technology Zimbabwe. The theory, conclusion and the common sources of error are extracted from the referenced sources.

Samson Svondo

savery chhin

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Flume model test on the behavior of debris flows into the reservoir and the impact pressure acting on the dam embankment

• Open access
• Published: 16 August 2024

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• Yusuke Sonoda   ORCID: orcid.org/0000-0003-0452-0428 1 &
• Yutaka Sawada   ORCID: orcid.org/0000-0001-5517-3345 1  

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The number of cases of damage to reservoirs due to debris flows has increased. In this study, granular material was released down the slope in a flume model to observe the debris flow morphology in a reservoir and to examine the impact pressure on a model dam embankment. The model flume had a slope angle of 30°, slope section width of 300 mm, and reservoir section width of 800 mm, and a model embankment with pressure and water pressure gauges was installed. Several experiments were conducted by varying the grain size of the granular materials to 3, 6 mm, mixed, and initial water storage levels. Observations from a high-speed camera indicate that when the debris flow enters the reservoir, the momentum rapidly decreases immediately after inflow. However, a solitary wave was generated, with heights reaching up to 2.5 times the initial water level. Additionally, during the impact of the debris flow on the model embankment, a large impact pressure was instantaneously generated. The magnitude and frequency of the occurrence tended to be more pronounced when the grain size was large. Additionally, the instantaneous impact pressure reached approximately twice the average impact pressure. However, with the exception of instantaneous large impact pressures, the existing equations used in the design of Sabo dams and coefficients with a specific range proposed in previous studies can be used to successfully calculate the impact pressure acting on the embankment in relation to the velocity.

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Introduction

Extreme weather events associated with climate change increase the frequency and damage due to debris flows owing to landslides and hillslope failures, seriously impacting structures and human life (IPCC 2023 ; Gariano and Guzzetti 2016 ). Small-scale fill dams that store water for agricultural use are often built in valleys or on steep slopes where water accumulates. Therefore, they are most seriously affected by debris flows. For example, in Japan, there are more than 150,000 small fill dams, termed as "Tameike", that store water for agricultural use (Ministry of Agriculture, Forestry and Fisheries 2024 ). In recent years, many cases have been reported in which debris flows or large amounts of sediment from upstream areas have caused fill dams to collapse. This in turn led to damage in downstream areas (Shoda et al. 2016 ). Safety assessments have been performed for earthquakes, floods, and leakages in many fill dams. However, they have not been performed for debris flows. Potential debris flow risks include the overtopping of inflow-generated waves and destruction of the dam embankment and ancillary structures caused by the impact. However, the lack of specific methods and findings for evaluating these risks implies that the safety against debris flows cannot be evaluated.

Previous research on debris flows and landslide masses entering a body of water include studies on the development and reach of tsunamis generated when debris flows and landslides enter large dam sites. For example, Miller et al. ( 2016 ) conducted a detailed study of tsunami height, velocity, and morphology, as well as run-up heights and sediment geometry in the far-field region when a landslide impacts water using a relatively large experimental flume and simulated debris flow (ceramic beads). Bullard et al. ( 2023 ) quantitatively evaluated the mobility of debris flow landslides using a similar experimental setup. Their research aimed to realize a more precise simulation of debris flows and elucidate the impact of mobility on the generated impulse waves. Additionally, Fritz et al. ( 2004 ) examined the characteristics of impulse waves in detail near fields by controlling a number of characteristics of inflow debris flows. Similar experiments have been conducted at different scales and with various granular materials, including studies using ceramic beads as described above, actual soil (Okura et al. 2002 ), solid blocks to investigate tsunami heights (Heller and Spinneken 2013 ; Sælevik et al. 2009 ), or using bagged granular materials (Evers and Hager 2015 ). Additionally, several studies have been conducted to elucidate the mechanism and behavior of debris flows (Bowman et al. 2009 ; Bryant et al. 2015 ; Iverson and Denlinger 2001 ). Iverson ( 2015 ) conducted almost real-scale debris flow experiments and discussed the influence of scale effects and boundary conditions on real phenomena and model experiments. Although the target was not debris flows, several studies have been conducted on impulse waves caused by snow avalanches, which have a lower density than landslides, similar to the study by Zitti et al. ( 2016 ). Many studies including numerical study have long been conducted in the field of dams installed on slopes as facilities to protect against debris flows (referred to as Sabo dams), most of which have focused on the impact pressure exerted by debris flows on dams and shape of the sedimentation (Miyoshi and Suzuki 1990 ; Shimoda et al. 1993 ; Zhou et al. 2019 ).

However, small-fill dams for irrigation, which are the subject of this study, differ significantly in their characteristics from the large dam sites and Sabo dams described above. First, earthen embankments and ancillary facilities have lower strengths than concrete structures. Additionally, the distance between the point of inflow of the debris flow and dam embankment is short; therefore, there is a high possibility that the debris flow will physically impact the dam embankment. Based on this point of view, it is essential to identify the risk of overflow and impact pressure at the time of debris flow inflow to evaluate the safety of facilities. However, there is a paucity of studies on these facilities with the exception of the studies by Shoda et al. ( 2021 , 2024 ). In these studies, useful information was obtained on the loading exerted on embankments by debris flows using experimental flumes. However, the behavior and impact pressure of debris flows during inflow have not been fully clarified because of the limitations of the experimental flume geometry (uniform flume width for the slope and reservoir). In addition, the water storage area where the water is located and the effect of the reservoir water-level have not been examined.

In this study, model tests were conducted in an experimental flume with a widened reservoir area at several water levels and granular materials to investigate the behavior of debris flows at the inflow, particularly the wave heights generated and the effect of water storage on the momentum-reducing effect of debris flows. Furthermore, the impact pressure due to debris flows was measured, and the applicability of the existing equations used in the design of the Sabo dam to a fill dam with water storage was examined.

Experimental method

Experimental equipment.

Experimental flume

The experiment is conducted using an acrylic experimental flume, as shown in Fig.  1 . A schematic of the experimental apparatus is shown in Fig.  2 . The experimental flume consists of two sections: (i) a 3000-mm long and 300-mm wide slope inclined at 30°, and (ii) a 1000-mm long and 800-mm wide horizontal reservoir section with a model dam embankment installed in it. A polyvinyl chloride sheet covers the bottom of the slope and reservoir area. The granular material is released from the box in the upper part of the slope by manually opening the partition plate. Two laser displacement gauges are installed at intervals of 1500 mm on the slope flume (Fig.  2 ) to calculate the velocity at which the material flows into the reservoir based on the difference in reaction time.

A schematic of the experimental apparatus

Model dam embankment

The model dam embankment used in this experiment was made of solid polyvinyl chloride and fixed using bolts. As shown in Fig.  2 , the upstream side of the model, where the debris flow impacts, has a slope structure similar to that of an actual dam embankment. The model is placed 300 mm away from the lower end of the slope. The specifications are as follows: height, 200 mm; base width (in the flow direction), 350 mm; crest width, 50 mm; length (in the perpendicular to flow direction), 800 mm; and slope ratio1:1.5. In the embankment on site, the length is generally 4 to 15 times the height. In this experiment, the length of the model embankment is 4 times the height, which is not significantly different from the real embankment geometry. The slope ratio of the embankment was determined based on design guidelines (Ministry of Agriculture, Forestry and Fisheries of Japan 2015 ). Both pressure and water pressure gauges were installed at a height of 25 mm from the bottom of the centerline of the upstream slope of the model embankment (Fig.  2 ).

Granular material

Granular materials are spherical ceramic beads with a particle density of ρ s  = 3.6 g/cm 3 and diameters of 3 mm (white), 6 mm (black), and 10 mm (red). Although ceramic beads have a larger particle density than ordinary soil, the flow velocity generally satisfies the similarity rule. Although the similarity rule is explained in the later section, the Froude similarity (Iverson 2015 ) rule was employed in this study. Also, the uniform particle size of the ceramic beads makes them an easy material for evaluating the effects of particle size. Three types of material were used for the debris flow, with a constant weight of 15 kg for all of the tests: a single particle size material of 3 and 6 mm, respectively, and a mixed particle size material of 3, 6 and 10 mm in the same weight ratio. The volume of the material was 7.0 × 10 3 cm 3 . The granular materials were submerged in water before the experiment. Using a 3 mm or larger material eliminates the influence of the capillary effect, which is the attraction force between particles due to suction by water and allows conditions to be matched in each case (Take et al. 2016 ).

Experimental conditions

Experimental cases.

Nine experimental cases were conducted; six cases displayed as d3_h0, d3_h50, d3_h100, d6_h0, d6_h50 and d6_h100, were conducted with a combination of three initial water levels of h  = 0 mm (no water), h  = 50 mm, and h  = 100 mm for each single grain size material ( d  = 3 mm and d  = 6 mm), and three cases displayed as dM_h0, dM_h50 and dM_h100, were conducted with three different initial water levels using a mixed particle size material of 3, 6 and 10 mm with the same mass (5 kg each). The case names for each condition are listed in Table  1 .

Measurement

In this experiment, the impact pressure acting on the dam embankment during the inflow of debris is measured using pressure and water pressure gauges attached to the model dam embankment, as shown in Fig.  3 . The values measured by the pressure gauges were classified into three categories: (i) impact pressure due to the granular material itself, (ii) hydrostatic pressure variation due to water level fluctuations, and (iii) hydrodynamic pressure due to the movement of stored water. Given that the impact pressure due to granular materials affect the failure and deformation of the embankment and its ancillary structures (e.g., inclined conduits and gates), the impact pressure P due to the impact of granular materials was evaluated by subtracting the value measured by the water pressure gauge at the same location from the value measured by the pressure gauge.

where P denotes the impact pressure owing to the granular material, p denotes the value measured by a pressure gauge, and u denotes the value measured by a water pressure gauge.

Measurements

As shown in Fig.  3 , the velocity v inflow of the front edge of the debris flow immediately before flowing down the slope and entering the reservoir was calculated based on the difference in the reaction time of the laser displacement gauges installed on the slope flume. Additionally, the debris flow behavior in the reservoir was captured using a high-speed camera (NAC Image Technology, Inc.). The frame rate was set to 2000 fps, and the shooting was synchronized with the measurement of the impact pressure. The velocity of submerged debris flow was measured using high-speed camera images. The bottom of the slope was set at x  = 0 mm and x -axis increased toward the embankment model (Fig.  3 ). First, the number of frames captured by the high-speed camera was counted until the front edge of the submerged granular material reached x  = 50 from 0 mm. Therefore, the velocity between x  = 0 and 50 mm could be calculated using this counted frames, set frame rate and distance between x  = 0 and 50 mm. This is defined as v 50 . Similarly, the velocities from x  = 50 to 100 mm were calculated as v 100 , v 150 , v 200 , and v 250 . As shown in Fig.  4 , in the case of water storage, the front edge of the submerged granular material could be observed because it moved relatively uniformly. Conversely, in the case without water, the particles moved in separate pieces, and it was difficult to observe the front edge of a body. Therefore, a single particle was tracked, rather than tracking the front edge of the granular body.

Tracking point for calculating velocity of debris flow

Examination of the similarity rule

The geometric scale of the experiment was set to 1/20. According to Mizuyama ( 1979 ), the interparticle friction force, which is the most dominant force in the motion of sand-gravel-type debris flows, satisfies the Froude law. Furthermore, the equations for the momentum of the debris flow also satisfy the Froude law. Therefore, in this experiment, the similarity rule for the Froude number (Iverson 2015 ), which is the velocity similarity rule, was considered in the model experiments. However, given that ordinary water is used in the reservoir, the Reynolds number, which is the ratio of inertial to viscous forces, is not the same for the prototype and model. Hence, it is smaller than that of the prototype, and the viscous force is relatively large.

The velocities of debris flows vary widely, and the average velocity of sand-gravel-type debris flows is generally estimated between 5.5 and 11 m/s (Ministry of Land, Infrastructure, Transport and Tourism 2008). In relatively mountainous upstream areas where the slope is steep, the velocity of debris flows is considered higher and velocities of 15 m/s have been measured (Prochaska et al. 2008 ; Murano 1965 ). Considering the 1/20 scale of the experiment, the velocity of the model, which satisfies the similarity rule, was 2.5–3.4 m/s. The velocities measured in this experiment were set 3.2–3.7 m/s, which will be described later. Although the velocities were slightly higher owing to the use of beads, they did not deviate significantly from the similarity rule.

Experimental results

Debris flow morphology observation.

When a debris flow enters a reservoir, it is expected to reach the dam embankment with a thin profile and retain momentum in the absence of water storage. Whereas in the water storage, its behavior changes because of a certain amount of resistance. In this section, we focus on the changes in the morphology of the debris flow and generated waves. Figure  5 shows images of cases, d3_h100, d6_h100 and dM_h100, immediately after the inflow of debris flows until the time of impact on the dam embankment. Immediately after the inflow, the water surface was not significantly affected by the inflow of debris. No water droplets were scattered in all cases, thus maintaining the thin shape of the debris flow as it flowed down the slope. Subsequently, at the front edge of the debris flow, water entered the pore spaces between the particles, indicating that the shape of the debris flow changed as if it were swelling. Simultaneously, the water level gradually increased, forming a stable solitary wave. The expansion of the front edge immediately after inflow and formation of solitary waves were similar to those in the model experiment conducted by Miller et al. ( 2016 ). Figure  6 shows the relationship between the maximum water level of the solitary wave, H max , and the initial water level, h . The ratio of water level rise is 2.3–2.6 times for the h  = 50 case and 1.4–1.7 times for the h  = 100 case. These results indicate that the rate of increase in the wave height tends to be greater when the initial water level is low. Although a more careful discussion is required for a quantitative evaluation, this implies that even if the water level is low, the inflow of debris flows may cause the water level to rise significantly, increasing the risk of overflow if the embankment does not have sufficient freeboard.

Images of granular materials flowing into the water reservoir

H max / h :Maximum wave height relative to initial water height

Impact mitigating effect of stored water

Table 2 presents the leading-edge velocity of the debris flow at the lower end of the slope (before entering the reservoir). Cases d3 and dM exhibit approximately the same velocity, whereas d6 exhibits a slightly higher velocity. However, the difference is approximately 12%. Figure  7 shows the reduction ratio of velocity, which is defined as the reduction ratio of velocity v x in the horizontal section to velocity v inflow at the inflow in each case. The horizontal axis indicates the distance from the lower end of the slope (Fig.  3 ).

Reduction ratio of debris flow velocity

In the case of no water storage, the debris flow reached the embankment with a slight velocity deceleration. Conversely, in the case of water storage, the velocity was significantly reduced to less than 50% immediately after inflow, indicating that the impact-mitigating effect of the stored water was significantly enhanced. However, given that there was little difference between the initial water levels of 50 mm and 100 mm, it is considered that the momentum-reducing effect of water storage did not differ above a certain level of water storage. Comparing the reduction ratios for x  = 200 and 250 mm for cases with storage water in Fig.  7 , d3 and dM are slightly smaller than d6, indicating a greater slow down. Figure  8 shows the particle deposition immediately after the experiment. The images on the left side of the figure shows the case with d3 particles, the center with d6 particles, and the right side with dM particles. The upper row of images shows the cases without water storage ( h  = 0), and the lower row shows the cases with water storage ( h  = 100). In the case with water storage, d3 particles (white) are deposited more upstream, whether the material of mixed (dM_h100) or single (d3_h100) particle size. Whereas in the case with d6 particles only (d6_h100), no such trend is observed. These results indicate that the momentum-reducing effect of the water storage was greater on the fine particles. Some experimental results (Bowman and Sanvitale 2009 ) show that the mobility of particle aggregations, such as debris flows, decreases with decreasing particle size below a certain value, but further investigation is required to clarify the mechanism in more detail.

Images of granular material deposition at h  = 0 mm and h  = 100 mm for each case

Impact load

Calculation of load components due to granular materials.

As explained in Eq. ( 1 ), the pressure measured by the pressure gauge included variations due to the water pressure. In previous studies (e.g., Shoda et al. 2024 ), loads were measured including both of the above. However, in the present study, only the impact pressure due to granular materials, which significantly contributes to the failure and deformation of dam embankments and ancillary structures, such as inclined flumes and gates, was evaluated by pressure. The impact pressure was evaluated by subtracting the value measured by the water pressure gauge at the exact location from that measured by the pressure gauge.

Figure  9 shows the change in impact pressure P over time (the value of the pressure gauge minus the value of the water pressure gauge) measured in each case. The data were low-pass processed with a threshold value of f based on Scheidl et al. ( 2013 ). The threshold value f was calculated as follows:

where f denotes the threshold value of the low-pass filter, v denotes the flow velocity of the granular material, and w denotes the width (diameter) of the pressure gauge receiver surface.

P : Impact pressure by granular materials: The data were low-pass processed with a threshold value of f indicated in Eq. ( 2 ) , referring to Scheidl et al. ( 2013 )

The change in the impact pressure due to the granular material over time showed a significant difference in the frequency of instantaneous large impact pressures between cases d3 and d6. In case d3, in which the grain size was 3 mm, such an instantaneous large impact pressure did not occur. Conversely, the frequency increased as the grain size increased. Fukuda and Fukuoka ( 2017 ) indicated that the instantaneous large impact pressure in debris flow disasters increases in frequency as the grain size increases, and this can occur in actual debris flows with the impact of huge stones and other objects. In the case of dM, where beads of three different grain sizes are mixed, the change and magnitude of the impact pressure are very similar to those in case d3 and instantaneous large impact pressures occur less frequently. The behavior of a granular material consisting of a mixture of different grain sizes in the same mass is strongly influenced by the behavior of smaller grains. However, the magnitude of impact pressure with h  = 0 should be carefully discussed in each case. As shown in Fig.  7 , the velocity immediately before the impact with the dam embankment differs by a factor of two or more between cases with h  = 0 and h  = 50 or 100. Conversely, the magnitudes of the impact pressures were not significantly different. This may be due to the fact that in the case of no water storage ( h  = 0), the momentum of the particles after impacting the embankment is too strong to be fully measured by the pressure gauges on the dam embankment slope as the particles bounce upward.

Based on the change in data over time, the maximum value of impact pressure, P max , and the average of the top 30 impact pressures, P ave , are extracted and discussed. These values are based on the data (250 data) between t  = 0.25 and 1.5 s when the graph in Fig.  9 generally rises. The change data over time generally consists of 6 to 8 data pieces per wavelength, and the top 30 averaged impact pressures should not be considered as instantaneous large impact pressures. Instead, they represent fluid forces that continuously act on and affect the dam embankment and its ancillary structures. Figure  10 compares P max and P ave for each case, and it can be observed that P ave decreases slightly as the initial water level increases from h50 to h100. But the reduction rate is slight, indicating that the impact-mitigating effect of stored water above a certain level was small. Additionally, in the case of d3, the difference between P max and P ave is slight, whereas in the case of d6, P max is almost twice the maximum value of P ave . Case dM exhibited intermediate values between those of d3 and d6. This indicates that large instantaneous impact pressures may be exerted regardless of water storage, depending on the form and type of debris flow.

Maximum impact pressure and average of top 30 data

Comparison with existing equations used in the design of Sabo dams

Based on the momentum of the fluid, the impact pressure P of the debris flow was calculated using Eq. ( 3 ), where the empirical coefficient α is proposed by various values based on experiments and field investigations and is known to have a certain range.

where v denotes velocity, ρ denotes the bulk density of the debris flow, and α denotes the coefficient. For example, Wendeler ( 2008 ) proposed a range for α from 0.7 to 2.0 based on impact pressure measurements obtained in laboratory experiments. Zhang ( 1993 ) proposed a range of α from 3.0 to 5.0 based on field measurements of over 70 actual debris flow sites. Furthermore, some studies also suggest α  = 2.0 for fine-grained materials (Watanabe and Ike 1981 ). In the design of Sabo dams for protecting against debris flows, the bulk density of debris flow, ρ , is calculated by the following Eq. ( 4 ) using the debris flow concentration, C .

Although various values have been proposed for the earth flow concentration C (e.g., Takahashi 1978 ), the standard design for the Sabo dam (National Institute for Land and Infrastructure Management, Ministry of Land, Infrastructure, Transport and Tourism 2016 ) generally states that it varies between 0.3 and 0.54 depending on the slope, with 0.3 for slopes of up to 10° and 0.54 for slopes of 16° or greater. Although a slope angle of 30° employed in this study is not assumed, the maximum value of C  = 0.54 was used. Concurrently, additional studies are required to determine how C should be set for behavior after inflow into the horizontal section.

Figure  11 compares the values of P max and P ave measured in this experiment with those calculated using Eq. ( 3 ). As the measured pressure was perpendicular to the slope, P was calculated by substituting the velocity component perpendicular to the slope in Eq. ( 3 ). The lower and upper ends of the bars in the figure represent the values when α  = 1.0 and α  = 3.0, respectively. Furthermore, P max is plotted slightly above the bars in some cases, while P ave is within the range of the bars between α  = 1.0 and 3.0 in many cases between α  = 1.0 and 2.0. Hence, with the exception of instantaneous large impact pressures, the impact pressure exerted by a debris flow into a reservoir can be successfully calculated in relation to velocity by appropriately setting α , as suggested in previous studies.

Comparison of existing equations and experimental data

In response to the increasing frequency of debris-flow disasters, model hydraulic experiments were conducted to investigate the behavior of the inflow of debris flows into fill dams located in valleys or on steep slopes, the momentum-reducing effect of water storage, and the impact pressure caused by granular materials. The following is a summary of our findings.

When a debris flow enters the reservoir, it rapidly reduces momentum immediately after the inflow. However, a solitary wave was generated, with heights reaching up to 2.5 times the initial water level.

Smaller grain sizes were more sensitive to the impact mitigation effect of stored water. However, no significant changes were observed above a certain water level.

The impact pressure on the dam embankment due to granular materials was instantaneous and large. However, the magnitude and frequency of the occurrence tended to be more pronounced when the grain sizes were large. The instantaneous impact pressure reached approximately twice the average impact pressure.

With the exception of instantaneous large impact pressures, the existing equations used in the design of Sabo dams and coefficients within a specific range proposed in previous studies can be used to successfully calculate the impact pressure acting on the embankment in relation to the velocity.

This study demonstrates the applicability of existing equations for calculating the impact pressure used in the design of Sabo dams and effects of water storage on debris flows into small-fill dams, which have rarely been studied. Furthermore, the influence of the scale of the experimental equipment and the use of ceramic beads as granular materials should be considered. For further clarification and quantitative evaluation of these phenomena, a numerical analysis using the results of this experiment as a benchmark is required.

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Acknowledgements

This study was supported by JSPS KAKENHI, Grant Numbers 21H02306 and 22KJ2235.

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Sonoda, Y., Sawada, Y. Flume model test on the behavior of debris flows into the reservoir and the impact pressure acting on the dam embankment. Paddy Water Environ (2024). https://doi.org/10.1007/s10333-024-00997-3

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Received : 17 April 2024

Revised : 18 July 2024

Accepted : 20 July 2024

Published : 16 August 2024

DOI : https://doi.org/10.1007/s10333-024-00997-3

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